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anygoal [31]
2 years ago
9

Please assist me with this question

Mathematics
1 answer:
docker41 [41]2 years ago
4 0

Answer:

? = 45

Step-by-step explanation:

the inner and outer triangles are similar ( AA postulate )

Then the ratios of corresponding sides are in proportion, that is

\frac{56}{56+24} = \frac{105}{105+?}  , that is

\frac{56}{80} = \frac{105}{105+?} ( divide numerator/denominator by 8 to simplify left side )

\frac{7}{10} = \frac{105}{105+?} ( cross- multiply )

7(105 + ? )  = 1050 ← distribute parenthesis on left side

735 + 7? = 1050 ( subtract 735 from both sides )

7? = 315 ( divide both sides by 7 )

? = 45

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